Thermomechanical responses of an imperfectly bonded multi-layered structure resting on an elastic foundation

Abstract

A new analytical model is developed for predicting responses of a multi-layered structure resting on an elastic foundation and subjected to general thermomechanical loading. The structure is composed of an arbitrary number of thin layers of dissimilar materials that are imperfectly bonded. Poisson’s ratio effects are incorporated through an extended Bernoulli–Euler beam theory. Imperfect bonding between adjacent layers is represented using a slip-interface model, which allows tangential slipping but requires the normal displacement and traction continuities across each interface. A Winkler foundation model is employed to capture elastic foundation effects. The analytical formulation is facilitated by a newly constructed state-space method, which converts the governing equations consisting of coupled second- and fourth-order ordinary differential equations (ODEs) to a system of first-order ODEs that is systematically solved using the eigenvalue problem method. To illustrate the new model, closed-form solutions for two example problems of two- and three-layer structures are derived. In addition, a simply supported seven-layer structure (transistor) resting on an elastic foundation is analyzed by directly applying the new model. The effects of interfacial and foundation stiffnesses on thermomechanical responses of the three sample structures are examined through parametric studies. The predictions by the current model agree well with those by an existing model without the foundation and with the simulation results from a finite element model constructed using COMSOL. These validate the new model and demonstrate its capability to predict the deflection, curvature, axial strain and stress, and interfacial normal and shear stresses in an imperfectly bonded multi-layered structure resting on an elastic foundation.